Terminator (solar)
The day-night boundary is the boundary between the illuminated by a star like the sun light side and the unexposed dark side of a celestial body, such as a planet or moon. The sight of this light - shadow boundary on the light coming from the celestial body reflected light is called in astronomy and meteorology also Terminator (Latin delimiter ') or separator (Latin delimiter' ).
The location of the dividing line relative to an external observer determines the phase of the celestial body and its shining light, such as the lunar phase. Are measured Terminator and phase with the phase angle; whose magnitude is, at 0 ° and full phase ( as the full moon ), at 90 ° dichotomy or half phase ( so half moon) and at 180 ° new phase ( so new moon).
Basics
Light and shadow boundary
Illuminated light source a body, so are all areas of its surface in the shade, which can not be achieved directly from the light. The contour of the projection of light forms on a spherical body near a great circle based in geometrical optics as a separator and in atmospheric optics and visual astronomy on a celestial body as a terminator or day - night boundary (english terminator, day / night boundary, also day night terminator ) is called. From a location other than where the light source or the body of view, this line appears as a delineation of the light side of the dark side on the image of the body, the saw disc.
On the surface of a celestial body decides on the light / shadow boundary, whether the light source can be seen or not - whether it is day or night. So it is not tags - - called twilight, when it is not the same at night quite dark in the distinction of day and night on earth periods of time during which the sun is no more or just not able to see straight. These transitions are the result of refraction and especially scattering of sunlight in the atmosphere, making the day - night boundary is not issued sharp but lapsed night side is a zone with a width of up to several hundred kilometers, the twilight zone, depending on the angle of incidence of the sun and of the density of the air layer; the terminator of the earth is therefore represented as a fuzzy line. In contrast, there are about no atmosphere on the moon, so also no twilight, and when the sun has set, it is suddenly dark; the terminator of the moon so shows sharp light / shadow boundaries on the surface relief.
The border, divorced with the locations on the surface of the Earth or a celestial body are those which can be reached directly by light (day) and those for which this is not true ( night), now is not so fixed, secretes it changes their course dependent on the movements of the round and the self-rotation. Path, axis tilt, direction, and the respective speed of rotation around the central star and the rotation because determine themselves as the current position of the day - night boundary as then their progressive change.
On Earth, the boundary between day and night near the equator moves at about 1670 km / h west and reached after about 24 hours later in the same position at the same place. The length of time for this one cycle of day and night ( day - night cycle ) for all places on earth are equal if they are not in the polar regions. In the latitudes beyond the polar circles namely it can happen that during this period there has been no change between day and night - because the day - night boundary has a place not happen.
The day - night boundary borders the exposed area of the surface and sets it on the unexposed. The change of their course, their progress or procedure, defined by the passages for a given location the beginning and end of the clear day - the one in the change from night to day and the second in the change from day to night. In relation to the earth's surface, the shift of the day - night boundary thus determines when and where the sun rises and sets. For the geographical location that is now: if, when and how long there is daylight, so the length of the day as the duration of bright day.
In sight of the outside, the day - night boundary represents a terminator which depends on the positions of the anstrahlenden star S, the illuminated object O and the observer B to each other - the solid angle of their constellation - on the observed disc shows a characteristic geometric shape and so marks the particular phase. Changes due to movements of S, O or B this angle, then shifted the Terminator and forms another figure of the shining light, indicates a different phase. However, without reflected light no terminator to see how, for example, the phase of the new moon.
Intrinsic rotations of the illuminated body can only be shown if its any atmosphere or the surface because having differences - for example, a relief - that stand out in this image of the disk, whether in details of the boundary line shown or to changes in the rate of discarded amount of light, the albedo.
In astronomical parlance the terms " day - night boundary " and " Terminator " are often used as synonyms, since they refer to the same light / shadow line; but the actual course of the border on a three-dimensional body and her image on a two dimensional disk are not the same.
The difference emerges clearly if one imagines a body without a reflectivity (albedo = 0), ie its surface back throws no light, or because a so-called black body, the electromagnetic radiation completely absorbed at each wavelength. Places now divorced terms of exposure, there would thus day and night, its sides and a boundary between - - From a light source illuminated, would be on the surface of such a body - as well as on other bodies which would be out of focus when the body is still around an atmosphere would have, so that twilight zones were to appear. But from this day - night boundary would appear nothing in the outward appearance of the body. For it would indeed reflected no light, no reflection takes place and an illumination would therefore not be determined. An image of this body, the light- sensitive recorded picture: would show only a dark disk. Neither would be excited to see a terminator, nor to determine a particular phase. Could attract attention this disc only on a background that is not of the same darkness - for example at a occultation or eclipse - so much like the moon.
For understanding, it may thus be quite useful to distinguish between the exposure as direct beam path and the lighting as indirect beam path - or so because between the direct light relative to the body and the indirect light with respect to its image, so then between the original image and a image so now. between an event and its reproduction
This fundamental distinction has da Vinci made and they've Leonardo - in his time - understood as a qualitative difference in the nature of light: a light as " lucie ", which illuminates and a different light than " lume " that emanates from the Lit; precisely this approach is also based on the following quote:
" The moon has no light of itself, and sees the sun as much from him as much as they lit; and from this light we see so much, how much of it sees us "
Terminator of the Moon ( Earth's moon ) - Details of relief with craters; Mare Serenitatis as a darker area in the left foreground
Double Terminator on Mimas ( moon of Saturn I) - top solar terminator, right through reflection ( indirect sunlight ) of Saturn
Terminator of the Titan ( moon of Saturn VI) - fuzzy zone and appear its atmosphere. Cassini, April 2007
Phase angle Φ and phase k
Depending on the angle formed by the light source and the observer with respect to the celestial body illuminated, a large part of its different illuminated half visible to the observer as light shape of a particular phase. This relationship can be described mathematically through the angle in space, the phase angle, and also over the visible portion of the illuminated disc surface phase.
If the observer stood at the location of the light source or on the line of the projection axis, as would be the phase angle = 0 °, it would look exactly the illuminated half of the disc (ie illuminated portion 1 of 1 or 1/1) appeared fully illuminated, thus the phase would be = 1 and would be called, for example, the moon full moon full phase.
Other hand, new moon or new phase is phase = 0 (percentage 0/ 1 or 0 of 1 ), thus no part of the disk illuminated, the observer sees exactly on the unlit half and stands as the light source, that the celestial body exactly in between on a line is the phase angle has been set to 180 °.
The phase angle is thus measured between sun light source (S) and observer (B ) with respect to the celestial body as an object (O) at the apex - viewed from the object it is the angle that appear under the S and B:
If the distance values are known when viewing a distant object, the phase angle can be calculated from:
About the phase angle can specify both Terminator and phase.
The phase may, in addition, as already mentioned are also represented as the illuminated portion of the apparent total area, or be construed as a lighting defect:
Occasionally, the phase angle is based on the direction of [ -180 °, 180 °] and the cos Φ phase as in the interval [ -1, 1 ] specified, in particular for computer numerical calculations.
The phase angle is a solid angle - no angles in a spherical triangle; he is only exactly 0 ° or 180 ° exactly when the three objects lie exactly on a line. Since this is not practically occur, the phase angle reaches a minimal value is close to 0 ° or the maximum of almost 180 °.
The phase angle is on the line of sight from the heavenly bodies to the observer and corresponds to that of elongation, would be seen under the from the object viewed from the observer. The elongation seen by the observer on the other hand - ie the angle, appear under the object and the light source for it - certainly not the phase, but is needed for it to calculate the apparent distance of anstrahlendem star to heaven body and its visibility. In particular, can it at phase angles close to 180 ° amounts - and yes very low elongation for the observer - are now entering a passage and encounter the object in front of the light -giving star. Depending on the apparent size ratios, there is then partially to cover or is it even a complete concealment possible - examples are a planetary transit in front of the sun or the occultation of the sun by the moon ( eclipse ).
Main phases and phase cycle
The phases depend on the particular position of the observer to the celestial bodies like the sun as its constellation, and can regularly follow each other in a cycle; which related to the observation duration of an entire phase cycle is called the synodic period.
Depending on the phase angle, different phases, which are named after their shape light show; The following are also referred to as the main phase and the other set represents combinations (such as the Syszygien as positions in a common plane or on the same line).
- Full Phase, - Standing seen by the heavenly bodies from the sun and observer in the same direction in a plane, so the observer sees only the day side of the celestial body and the terminator falls on the outer edge of the disc seen. This phase is referred to as full. Then stand, for example, inner planet at superior conjunction, outer planets either in conjunction or in opposition, the moon is in opposition to an observer on Earth.
- Half phase - At a phase angle of 90 °, the observer sees the terminator so that it appears as a straight line. The disk is apparently divided into two halves, a semicircular dayside and a similar night side. This phase is also half-phase or dichotomy ( dĭchŏtŏmos cut in two, ') called; it does not occur on the outer planets. This position is not to be confused with the quadrature.
- New phase - When the phase angle is nearly maximal, are celestial bodies and sun seen from the observer in the same direction in a plane. Inner planets are then at inferior conjunction, the other planets and the moon is in conjunction, between the sun and the observer; they return him pretending to be their night side. The ( ecliptic ) elongation at Watchers is zero, so usually this phase forms in the subject use the zero point for the calculation of synodic periods. This phase is called only in relation to the moon new and otherwise remains unnamed; it is only possible if the heavenly bodies between observer and light source occurs as the Earth's moon or inner planet. The prefix, New ... ' is otherwise only Neulicht used in the description, for the narrow crescent moon and a half days after the new moon.
Between these main phases of the Terminator has the shape of an ellipse arc and gives the figure of light the familiar crescent shape or wrongly called " egg-shaped " outline, both before the full phase ( towards increasing) and after the full phase (her waning ) within a phase cycle.
The phase is usually given geocentric - ekliptikal: The times for the true observation on the Earth's surface each soft light from them, even for the exact date of the moon, new moon.
Geometric figure of the Terminator
A spherical body to the projection of light forms a circular surface, the edge is a circle. Its diameter is greater at point light source with increasing distance from the body and would be at an infinite distance - with parallel incident rays without distraction - his greatest, that of a so-called great circle. Thus, the exposed half of the sphere by an equally large unexposed hemisphere would be discontinued. The same division would also materialize at a surface light source radiating at right angles and as a disc with the same radius as the body is at a right angle to this - no matter the distance. The actual projection conditions can be understood as an approximation to these ideal cases and the incidence of light rays then simplified as approximately parallel respectively.
In celestial bodies without atmosphere light is neither distracted with incidence after reflection and so illuminated on a spherical body having a surface with a circular boundary, the reflected light then draws a picture as the sight of the body, in astronomy also disc (english disk) called.
Terminator - - depending on the distance of the observer and the angle at which the illuminated hemisphere is seen the boundary line appears in the image is now depending on the phase as a circle, an ellipse arc, a straight line or not. The disk rim as the outer periphery of the disc and the terminator as an internal division of the disc surface together determine the shape of a light illuminated celestial body, his vision or aspect. Depending on your perspective, or phase, the disk appears full, half or not illuminated when the terminator from the elliptical arc is now the circle or straight line or invisible. The main axis of that ellipse, appears as its arch of the Terminator is equal to the apparent diameter of the disc, the semi-minor axis is calculated approximately from times.
That a fine crescent moon sometimes seems hörnchenfömig is for Luna cornuta, as if the tips are bent inward, is to over-exposure effects ( irradiation ) and the elevation of contrasts by our visual perception; so the narrow bright moon shape is oversubscribed lifted from their different dark environment, on the one hand the night-black background, on the other hand, the earthshine from dimly lit portion of the moon. In addition, the moonlight is still scattered on the way through the earth's atmosphere. The croissant shape of Erdsichel on some recordings from space comes mainly through refraction and scattering effects into existence - so appear from space the snowy polar zones brightened and as an extended tips. Stronger still is the squirrel deception in Venus, which now also has an atmosphere, but the dark side is always invisible because it does not receive any reflection of a nearby celestial body.
The ideal shadow boundary can be calculated ( program code: C) as follows:
Xscale = cos (2 * PI * ph) for (i = 0; i < RADIUS; i ) { cp = RADIUS * cos ( asin ( (double) i / RADIUS) ); if ( ph < 0.5) { rx = (int ) ( CENTER cp ); lx = (int ) ( CENTER xscale * cp ); Else { } lx = (int ) ( CENTER - cp ); rx = (int ) ( CENTER - xscale * cp ); } } World map with day - night boundary, shortly after the ( northern ) spring equinox: At the North Pole there is already polar day. [ rx, i] ... coordinates of the dark disc edge [lx, i] coordinates of the terminator ... as Cartesian coordinates ( here: integer pixel by pixel) with:
Source: J. Walker's Moontool, according to Meeus / Duffett -Smith
With a projection on a map of the terminator or separator then assumes more complex shapes. Projected on a plat map shows the light / shadow boundary line arched a course in the form of a distorted sine curve and can decay to the date of the equinox in two parallel lines.
Moreover, the actual conditions are to be considered, under which the day - night boundary but only approximately forms a great circle or the Terminator an ellipse with semi-major axis of only virtually whose radius: Because emanating from a point source beams do not illuminate quite a half of a sphere, refractions in an atmosphere shift the boundary line, scatter, they make out of focus, and extensive stretches of light source - like the sun - lead to the incidence of light from different angles or may illuminate more precisely than a hemisphere. However, light rays may be compared by the sun due to the large distance to the diameter of the illuminated celestial bodies are assumed to be incident parallel to a general astronomical observations.
Sky Mechanical aspects
A star rises on the illuminated celestial bodies a page on the light out and on the shade. The delineation of light and shadow side is viewed depends on the location of the observer under two fundamentally different points of view:
In observing the external perspective, the reflected light of an illuminated celestial body, the light - shadow boundary is the terminator, which determines the appearance of the light shape. Within the disk circumference, he is light on dark and so marks the phase. This aspect is dependent on the solid angle constituting the star and celestial bodies with respect to the observation site, for example, sun and moon to earth. In their rotations around its own axis, this angle is most effective, but probably in the movements of the moon and of the earth as a run around the sun. The resulting changes in phase shows up on the observed lunar disk as a shift of the terminator. A continuous series of such phase changes to the repetition forms a phase cycle; in this case also means the month.
In the internal perspective, as exposed directly on the surface of the illuminated celestial body of the light source, the boundary between light and shadow to the day - night boundary that determines a location of the surface if it is exposed and direct light can reach the ground. There, like shapes live, whose activity is influenced by light energy - be it that they avoid the harmful effect or that they make energetic effects usable for itself. Whether for that day or night, depending on the angle, the star and the surface of the celestial body forming with respect to the location of the observer. On Earth, it would be the height of the sun above the sea on a beach. During the rotation of the earth in the orbit change this angle, and during its rotation around its own axis. By the day - night boundary is moved on the earth's surface; the continued shift with two changes between light and dark, to the repetition of a similar exposure phase in the same place then forms a full day - night cycle, which is also called a full day.
The day - night boundary may shift when the body is in motion. Delivery he doing around the light source without its own rotation, so the light / shadow boundary moved during a full round twice over its surface. A tag night cycle would have expired for a stationary observer on this body then, the long lasted just like a year on this track. Suppose that the body would now rotate exactly once during a period of revolution around itself - and this to an axis that is perpendicular to the orbital plane - so there are two possibilities. It rotates in the same sense in which he runs around, then he turns the umlaufenen light source continuously to the same page. In such a bound rotation takes his day so: if not forever, then for so long, until the star disappears as the light source - if the body still exists. If turns but in the opposite direction to the direction of rotation, then now is his year of two days ( and two nights). So, depending on whether the self-rotation direction coincides for a body with the direction of rotation in orbit or not, can thus for an orbital period in his year, either drop a day away or to come a day. In other words: The number of complete rotations own is never equal to the number of days relative to the central star, but either plus or minus one within a year. In the case of the earth means that a solar day does not correspond to a whole period of rotation, but about 1/365 because missing.
If the axis of rotation of the celestial body would be exactly perpendicular to its orbital plane, ie, with an inclination equal to zero, the day - night boundary verliefe exactly through both poles. In this case there would be in terms of latitude on this celestial body no difference in the time of day or night, because within a solar day, the day-night limit would be exceeded twice for all locations. If the axis of rotation but is not exactly perpendicular to the orbital plane of the celestial body, the time periods of the day or night sparse change from one day - night cycle to the next. The differences that occur during a run around the sun The farther a place is from the equator, the greater. Around the poles is there even regions of the surface, is not exceeded within which the day - night boundary in some rotation periods. The boundaries of these areas define the polar circles.
Terminator Earth
On the way through the atmosphere light is refracted and scattered, so that as the result of refraction (refraction ) by about half a degree then reaches a wider area of the earth's surface and next to twilight zones occur because of scattering. The light / shadow boundary on the globe sums so tagseitig a larger area than other night and night is also hand out of focus.
Part of the light is reflected back from the exposed surface (reflection ), as diffuse reflection - depending on surface texture and angle of incidence a different portion. This albedo of the earth totals currently about one-third ( 31% ) of the incident sunlight, with significant differences in albedo, for example, of new snow blankets (approx. 85%) and of water levels at angles above 45 ° (about 5 %). The reflected light passes through the atmosphere then a second time with refraction and scattering before a picture of the day - night boundary is designed as a terminator on the Earth disk - seen from the outside perspective from space.
The rotation axis of the Earth is not perpendicular to the orbital plane, but at an angle of about 66.5 °, the obliquity of the ecliptic amounts to about 23.5 °. During the terminator by a point on the equator travels yet pretty much every 12 hours, so take lights there day and night of equal length, the effects of the obliquity term already in temperate latitudes significant differences in the lengths of day and night.
At the solstices, or solstices are in summer on the northern hemisphere, the daylight longest (summer solstice, around June 21 ) - as in the Southern Hemisphere then nights - and in the winter the days are shortest ( winter solstice, around 21 December) - while in the southern hemisphere then is the longest day. In each case, about a quarter after these dates are lights day and night of equal length ( or equinox equinox, around March 20 or around 23 September ). The day lengths vary in moderate latitudes, for example, of about 45 ° between 8 hours and 16 hours, corresponding to the night lengths. From about 66.5 ° north or south latitude, the polar circles, then polar days with midnight sun or the polar nights can occur.
Against the poles out so does the duration of twilight - it is already at 45 ° width of up to one and a half hours when astromonische dusk around the winter solstice; transferred to the soil surface, this corresponds to a zone of about one hundred kilometers and therefore the so-called white nights occur even in widths below the Arctic Circle on.
The diverse phenomena of sinking and rising of the sun arise as astronomical phenomena through scattering and refraction in those layers of the atmosphere, which are now cut up by the geometric terminator plane.
Seasonal variation of the day - night boundary, based on the Ekliptikalebene
Day - night boundary of sunset during the year, but now shown geostationary for Central Europe
Seen from ISS in the plane of the terminator from: sunset, diffused light illuminates the atmosphere
Terminator of the moon
When the sun has gone down, it is on the moon suddenly dark - but the sun takes on the moon by the slow rotation of several hours. The Terminator but forms a sharp line. From Earth, can the migration of the day - night boundary of the moon track very well: It lasts for a month, a span of the moon phases of full moon - waning crescent - moon - increasing Crescent - until the full moon. In this synodic lunar month the Terminator moves a few degrees every night before (an average of about 12.6 ° in 24 h).
Here is the shadow line of the moon, which is approximately perpendicular to the ecliptic, as seen from the middle latitudes of the Earth from mostly so that the moon shines from or increase respectively to the left or right. An exactly horizontal to the horizon lying crescent moon, also called Mondschiffchen can be seen from the equatorial regions closer beneath nearly 29 ° of latitude from when the moon's orbit is perpendicular to the horizon. Even at a higher latitude likes a good 5 ° inclined to the ecliptic plane of the path of the moon is still relatively steep positions reach the horizon - fluctuating around 10 ° in the course of nearly 19 years and a maximum for large moon turning - but no vertical appears more and so a crescent moon lying most appropriate because something tipped. Only very fine sickles can be seen lying horizontally under special conditions at high ecliptic latitude of the moon.
Opposite sites of the Northern Hemisphere shows the moon figure considered now in reverse horizontal orientation in the same phase of the Southern Hemisphere ago - not because of the terminator, which has almost the same position, but because of the observer relative to the Europeans is, or vice versa on the head and both the same shining light of the moon ever situate in their topocentric reference system with different zenith. So the waning moon appears to have the others to the right to the left and the One.
A common, the moon observer common deception is that, for example, the half- moon does not seem culmination to point exactly to the sun, then just stands below the horizon, but supposedly has it: The straight line joining Sun Moon is our to the horizontal plane as basis related projection dome of the sky to a curved line.
If the phase angle is not exactly 0 °, the heavenly bodies appear not fully enlightened. The moon is also about full moon not fully illuminated, typical values are at 99.96 %; only at very small ecliptic latitude - as with the lunar eclipses - he would come close to its maximum possible illumination, but then he is so darkened by Earth's shadow and is not fully illuminated by therefore.
The theoretically visible very narrow crescent just before or after new moon phase is indeed difficult to perceive, because then the moon is very close to the daytime sky with the sun and so with her and is outshone - except for a very brief period in the early dawn just over the horizon. The sighting of this last time or the first time to be seen crescent forms the basis of many clock and calendar accounts, so as Altlicht the ancient Egyptian as for when the Neulicht of today's Islamic calendar. The sun is remote part of the moon is visible to us as reflections of sunlight on the Earth and its atmosphere, the Earthshine, the moon shine on indirectly and so let the erdzugewandte dark side of the moon not quite in the dark. The fact that the crescent moon can be seen sometimes as a croissant -shaped, Luna cornuta is called.
Great importance is the terminator of the moon for the selenography ( moon mapping ): The crisp Line breaks up on its edge in numerous edges of the craters and other surveys that have just lit on the day - night boundary in the shadow region as bright arcs of the unilluminated lunar surface lift or already are in the darkness and are emerging as a darkening in the dayside. Until the 2000s into detailed drawings of shadows and their distortion were the only way to determine the three-dimensional topography of the moon in cards. Since the Lunar Orbiter missions and the now high-resolution photographic potential mapping of the moon nurmehr group of committed amateur astronomers are working according to this method in order to clarify questions of detail on individual surface shapes. Only with probes such as the Chinese Chang'e -1 in 2007 and the Lunar Reconnaissance Orbiter 2009, which were equipped with stereo photography and laser scanning for altimetry, the detailed topography of the moon no longer from the visual observation is dependent terminator.
The same conjunction of December 1, 2008, Australia
Detail photo of the moon (mosaic from 5 shots) February 10, 2008, France
The same, overexposed: Clearly some deviations from the ideal elliptical shape